Question

shiw that only one out of n,n+2,n+4is divisible by 3,where n is any positive integer
@hartnn @Rohith15

Answer 1

@jbreezy622

Answer 2

If n is divisible by 3 there is nothing more to prove. Suppose that n is not divisible by 3 Then the remainder of dividing n by 3 is either 1 or 2. In the first case n+2 is divisible by 3; in the second case n+4 is divisible by 3.

Answer 3

@Rohith15 cud u plzz write with the steps sir

Answer 4

What type of proof techniques have you been learning about in class?

Answer 5

Suppose that n is divisible by 3. Then, we can write:
n = 3k, for some integer k.

Then, n + 2 = 3k + 2 and n + 4 = 3k + 4 are both not divisible by 3 since:
(n + 2)/3 = k + 2/3 and (n + 4)/3 = k + 4/3 = (k + 1) + 1/3,

which shows that n + 2 and n + 4 leave remainders of 2 and 1 respectively when divided by 3.

In a similar fashion, if n + 2 is divisible by 3, then:
n + 2 = 3k, for some integer k.

Then, n = (n + 2) - 2 = 3k - 2 and n + 4 = (n + 2) + 2 = 3k + 2 are both not divisible by 3 (this can be shown similarly to the above). In a similar fashion, if n + 4 is divisible by 3, both n and n + 2 are not divisible by 3

Answer 6

@Rohith15 didnt get it

Answer 7

There is a very elegant way to show this one.
n + 4 is divisible by 3 if and only if
n + 1 is divisible by 3

Answer 8

@surd First read it fully and then tell me where you didnt understand.

Answer 9

So proving this problem is equivalent to showing that either n, n+1, or n+2 is divisible by 3. (n+4 and n+1 are the same with respect to divisibility by 3)

Answer 10

plzz shiw statemen in some link or wirite it nsd show me plzz\

Answer 11

See, if n is divisible by 3 we can write n=3k right??

Answer 12

Now, showing that for three consecutive numbers is relative simple. If you divide by n, n+1, n+2, only one of them has a remainder of 0. So only is divisible by 3. That is simple conquence from that they are consecutive.

Answer 13

yup

Answer 14

sorry, if you divide n, n+1, and n+2 BY 3, only one of them...

Answer 15

I agree with you @Miracrown but you cant write it as a theorem right??

Answer 16

mira do you mind showing me all the steoppd plzz

Answer 17

@hartnn plzz go chek eng chat they nedd ur help

Answer 18

Why do think it couldn't be a theorem?

Answer 19

PLZZ SHOW ALL THE STEPS BEG UUU

Answer 20

That's your job. I've explained you how to do it, now what's left is for you to do.

Answer 21

@Miracrown plzz beg uuuuu